Other people survived in caves, so there's an option for him to survive. It could also be the reason he turned into a Ghoul. The cave protected him from the "fallout" but, the water that trickled into the cave was slightly irradiated and so that was the reason he turned, slowly.
OR he could have been in the subway tunnels at the time, in a bigger city, like DC and survived because he hid in a maintenance tunnel.
It really depends on where you want your character to start out. Is he a city kid, or more a country boy? I think you have an idea about the setting, since its based on the Fallout Universe. YOU need to think about your character, his personality, his goals, his motivations etc, the rest will become clear, once you know who tells your story.